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C*-semigroup bundles and C*-algebras whose irreducible representations are all finite dimensional

Thomas Müller — 1989

We investigate the structure of C*-algebras with a finite bound on the dimensions of their irreducible representations, sometimes called “subhomogeneous”.In the first chapter we develop the theory of C*-semigroup bundles. These are C*-bundles over semigroups together with a “structure map” which links the semigroup structure of the base space lo the bundle. Under suitable conditions we prove the existence of “enough” bounded sections, which arc “compatible” with the C*-semigroup bundle structure....

Asymptotic stability for sets of polynomials

Thomas W. MüllerJan-Christoph Schlage-Puchta — 2005

Archivum Mathematicum

We introduce the concept of asymptotic stability for a set of complex functions analytic around the origin, implicitly contained in an earlier paper of the first mentioned author (“Finite group actions and asymptotic expansion of e P ( z ) ", Combinatorica 17 (1997), 523 – 554). As a consequence of our main result we find that the collection of entire functions exp ( 𝔓 ) with 𝔓 the set of all real polynomials P ( z ) satisfying Hayman’s condition [ z n ] exp ( P ( z ) ) > 0 ( n n 0 ) is asymptotically stable. This answers a question raised in loc. cit.

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